how do you find the equation for the exponential function containing the points (0,4) and (2,17)?

Answer 1

If it's exponential, you know it will have the form
y = k.a^x for some k and a (equivalently, y = k e^(tx) for some k and t).
Taking y = k a^x, y(0) = k and y(2) = ka^2, so k = 4 and a = √(17/4). So y = 4 (17/4)^(x/2).